The present book is the second of several volumes which are intended to replace the Introduction to Theoretical Physics written by the same authors in 1933. By separating the material on mechanics, on electromagnetism, and on the quantum theory, we believe that it is possible to give a somewhat better rounded treatment of each of these fields, which will be more useful to the teacher and the student. We have taken advantage of the opportunity to give a considerably more complete treatment of the foundations of electrostatics and magneto-statics, and to introduce some of the new developments in electromagnetic theory since 1933. At the same time, we have tried to preserve, and even to extend, the general unity of treatment which we believed so important when the earlier book was published. We have a conviction that the teaching of theoretical physics in a number of separate courses, as in mechanics, electromagnetic theory, potential theory, thermodynamics, and modern physics, tends to keep a student from seeing the unity of physics, and from appreciating the importance of applying principles developed for one branch of science to the problems of another.